document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31632>Question 31632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3)	Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 <BR>\n" );
document.write( "•	16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2). <BR>\n" );
document.write( "•	v0 is the initial velocity (how hard do you throw the object, measured in feet per second).<BR>\n" );
document.write( "•	s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.\r<BR>\n" );
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document.write( "1.  	How long will it take to hit the ground?\r<BR>\n" );
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document.write( "2.	What is the maximum height of the ball?  What time will the maximum height be attained?\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18279 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the given function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+-16t%5E2+%2B+%28vo%29t+%2B+so ALIGN=MIDDLE  ALT=\"s%28t%29+=+-16t%5E2+%2B+%28vo%29t+%2B+so\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substituting vo = 64 ft/sec. and so = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+-16t%5E2+%2B+64t ALIGN=MIDDLE  ALT=\"s%28t%29+=+-16t%5E2+%2B+64t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set s(t) = 0 and solve for t to find the time at which the baseball will return to the ground.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%5E2+%2B+64t ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+64t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for t. First factor out a t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+t%28-16t+%2B+64%29 ALIGN=MIDDLE  ALT=\"0+=+t%28-16t+%2B+64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the initial condition when the height, s = 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t+%2B+64 ALIGN=MIDDLE  ALT=\"0+=+-16t+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 16t to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t+=+64 ALIGN=MIDDLE  ALT=\"16t+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 16.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4 ALIGN=MIDDLE  ALT=\"t+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Secs.<BR>\n" );
document.write( "1) The ball returns to the ground in 4 seconds.\r<BR>\n" );
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document.write( "The maximum height of the ball can be found by finding the location of the verttex of the parabola that is represented by the original quadratic equation<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+-16t%5E2+%2B+64t ALIGN=MIDDLE  ALT=\"s%28t%29+=+-16t%5E2+%2B+64t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The t-coordinate of the vertex is given by<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"t+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The a and b come from the standard form of a quadratic equation<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this problem, a = -16, b = 64, and c = 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-64%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Secs. This is the time at which the baseball reaches its maximum height.<BR>\n" );
document.write( "To find the maximum height, substitute this value of t into the original equation and solve for s.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+-16%282%29%5E2+%2B+64%282%29 ALIGN=MIDDLE  ALT=\"s%282%29+=+-16%282%29%5E2+%2B+64%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+-64+%2B+128 ALIGN=MIDDLE  ALT=\"s%282%29+=+-64+%2B+128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+64 ALIGN=MIDDLE  ALT=\"s%282%29+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >Feet.  This is the maximum height attained by the baseball. </SPAN>\n" );
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